Tokyo Journal of Mathematics

Zariski-van Kampen Method and Transcendental Lattices of Certain Singular $K3$ Surfaces

Ken-ichiro ARIMA and Ichiro SHIMADA

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We present a method of Zariski-van Kampen type for the calculation of the transcendental lattice of a complex projective surface. As an application, we calculate the transcendental lattices of complex singular $K3$ surfaces associated with an arithmetic Zariski pair of maximizing sextics of type $A_{10}+A_{9}$ that are defined over $\mathbf{Q}(\sqrt{5})$ and are conjugate to each other by the action of $\text{Gal}(\mathbf{Q}(\sqrt{5})/\mathbf{Q})$.

Article information

Tokyo J. Math., Volume 32, Number 1 (2009), 201-227.

First available in Project Euclid: 7 August 2009

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Zentralblatt MATH identifier

Primary: 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14H50: Plane and space curves 14H25: Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]


ARIMA, Ken-ichiro; SHIMADA, Ichiro. Zariski-van Kampen Method and Transcendental Lattices of Certain Singular $K3$ Surfaces. Tokyo J. Math. 32 (2009), no. 1, 201--227. doi:10.3836/tjm/1249648417.

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